Vol. 11, No. 9, 2017

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Elementary equivalence versus isomorphism, II

Florian Pop

Vol. 11 (2017), No. 9, 2091–2111

In this note we give sentences ϑK in the language of fields which describe the isomorphy type of K among finitely generated fields, provided the Kronecker dimension dim(K) satisfies dim(K) < 3. This extends results by Rumely (1980) concerning global fields; see also Scanlon (2008).

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elementary equivalence versus isomorphism, first-order definability, finitely generated fields, Milnor $K$-groups, Galois étale cohomology, Kato's higher local-global principles
Mathematical Subject Classification 2010
Primary: 11G30, 14H25
Secondary: 03C62, 11G99, 12F20, 12G10, 12L12, 13F30
Received: 23 April 2016
Revised: 11 May 2017
Accepted: 3 August 2017
Published: 2 December 2017
Florian Pop
Department of Mathematics
University of Pennsylvania
Philadelphia, PA
United States